# Mathematical Methods and its Applications - Institution: IIT Roorkee - Department: Mathematics - Taught by: Prof. S. K. Gupta, Prof. P. N. Agrawal - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111107098) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111107098) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) This course is a basic course offered to UG student of Engineering/Science background. It contains ODE,PDE, Laplace transforms, Z-transforms, Fourier series and Fourier transforms. It plays an important role for solving various engineering sciences problems.Therefore, it has tremendous applications in diverse fields in engineering sciences. INTENDED AUDIENCE : UG students of technical universities/colleges. ## Lectures 1. [Introduction to linear differential equations](https://invisiblenetwork.ai/learn/nptel/111107098/4aed3131e0b8) (YouTube) 2. [Linear dependence, independence and Wronskian of functions, Existence and Uniqueness theorem](https://invisiblenetwork.ai/learn/nptel/111107098/01090713b57c) (YouTube) 3. [Solution of second order homogeneous linear differential equations with constant coefficient-](https://invisiblenetwork.ai/learn/nptel/111107098/092fcd7249a4) (YouTube) 4. [Solution of second order homogeneous linear differential equations with constant coefficient-II](https://invisiblenetwork.ai/learn/nptel/111107098/51cc1e4d7ec8) (YouTube) 5. [Methods of Undetermined coefficients](https://invisiblenetwork.ai/learn/nptel/111107098/8123e300f4bf) (YouTube) 6. [Methods for finding particular integrals for second order linear differential equations with constant coefficients I](https://invisiblenetwork.ai/learn/nptel/111107098/e29458d3105c) (YouTube) 7. [Methods for finding particular integrals for second order linear differential equations with constant coefficients II](https://invisiblenetwork.ai/learn/nptel/111107098/bba5bdaa8a17) (YouTube) 8. [Methods for finding particular integrals for second order linear differential equations with constant coefficients III](https://invisiblenetwork.ai/learn/nptel/111107098/c231d40706ed) (YouTube) 9. [Cauchy-Euler equation](https://invisiblenetwork.ai/learn/nptel/111107098/1c5dc78f4828) (YouTube) 10. [Methods of reduction for second order-linear differential equations](https://invisiblenetwork.ai/learn/nptel/111107098/8e19a44eacda) (YouTube) 11. [Methods of variation of parameters](https://invisiblenetwork.ai/learn/nptel/111107098/f848df0d22b3) (YouTube) 12. [Solution of second order differential equations by changing dependent variables](https://invisiblenetwork.ai/learn/nptel/111107098/759ade69d55a) (YouTube) 13. [Solution of second order differential equations by changing independent variable](https://invisiblenetwork.ai/learn/nptel/111107098/210e19cd72c5) (YouTube) 14. [Solution of higher-order homogeneous linear differential equations with constant coefficients](https://invisiblenetwork.ai/learn/nptel/111107098/50c60e64de6f) (YouTube) 15. [Methods for finding particular integral for higher-order linear differential equations with constant coefficient s](https://invisiblenetwork.ai/learn/nptel/111107098/632b3d1b4151) (YouTube) 16. [Formulation of partial differential equations](https://invisiblenetwork.ai/learn/nptel/111107098/d1d86db229cd) (YouTube) 17. [Solution of Lagrange's equation I](https://invisiblenetwork.ai/learn/nptel/111107098/13887c2b3ddb) (YouTube) 18. [Solution of Lagranage's equations II](https://invisiblenetwork.ai/learn/nptel/111107098/4ba13d2bf32d) (YouTube) 19. [Solution of first order non-linear equation I](https://invisiblenetwork.ai/learn/nptel/111107098/9a981e5932be) (YouTube) 20. [Solution of first order non-linear equation II](https://invisiblenetwork.ai/learn/nptel/111107098/9ccc14f17401) (YouTube) 21. [Solution of first order non linear equation III](https://invisiblenetwork.ai/learn/nptel/111107098/358eb9991c52) (YouTube) 22. [Solution of first order non linear equation IV](https://invisiblenetwork.ai/learn/nptel/111107098/638347dd39cd) (YouTube) 23. [Introduction to Laplace transforms](https://invisiblenetwork.ai/learn/nptel/111107098/e2169f84c7e6) (YouTube) 24. [Laplace transforms of some standard functions](https://invisiblenetwork.ai/learn/nptel/111107098/abde50b4b012) (YouTube) 25. [Existence theorem for Laplace transforms](https://invisiblenetwork.ai/learn/nptel/111107098/1cd5f504eb17) (YouTube) 26. [Properties of Laplace transforms-I](https://invisiblenetwork.ai/learn/nptel/111107098/fb77acbad8ab) (YouTube) 27. [Properties of Laplace transforms-II](https://invisiblenetwork.ai/learn/nptel/111107098/af98e69b3548) (YouTube) 28. [Properties of Laplace transforms-III](https://invisiblenetwork.ai/learn/nptel/111107098/c6cd0fa00d8f) (YouTube) 29. [Properties of Laplace transforms-IV](https://invisiblenetwork.ai/learn/nptel/111107098/899b5971dd32) (YouTube) 30. [Convolution Theorem for Laplace Transforms-I](https://invisiblenetwork.ai/learn/nptel/111107098/b811e42dba43) (YouTube) 31. [Convolution Theorem for Laplace Transforms-II](https://invisiblenetwork.ai/learn/nptel/111107098/4ce6bb32a39a) (YouTube) 32. [Initial and Final Value Theorems for Laplace Transforms](https://invisiblenetwork.ai/learn/nptel/111107098/ee1e32f69f1d) (YouTube) 33. [Laplace Transforms of Periodic Functions](https://invisiblenetwork.ai/learn/nptel/111107098/cd5564624e6c) (YouTube) 34. [Laplace Transforms of Unit Step Function](https://invisiblenetwork.ai/learn/nptel/111107098/da5ad30d4f21) (YouTube) 35. [Laplace Transforms of Dirac delta Functions](https://invisiblenetwork.ai/learn/nptel/111107098/6cc4e51970ea) (YouTube) 36. [Applications of Laplace Transforms-I](https://invisiblenetwork.ai/learn/nptel/111107098/9ee17323c8f5) (YouTube) 37. [Applications of Laplace Transforms-II](https://invisiblenetwork.ai/learn/nptel/111107098/d3a6de6a65e1) (YouTube) 38. [Applications of Laplace Transforms-III](https://invisiblenetwork.ai/learn/nptel/111107098/cd9e9a65a371) (YouTube) 39. [Z- transform and inverse Z- transform of elemetary functions](https://invisiblenetwork.ai/learn/nptel/111107098/d3a925b001d8) (YouTube) 40. [Properties of Z-transforms-I](https://invisiblenetwork.ai/learn/nptel/111107098/542e7b741619) (YouTube) 41. [Properties of Z - transformatons - II](https://invisiblenetwork.ai/learn/nptel/111107098/32972eeca9b8) (YouTube) 42. [Initial and final theorems for Z- transforms](https://invisiblenetwork.ai/learn/nptel/111107098/0e824d921342) (YouTube) 43. [Convolution theorem for Z-transforms](https://invisiblenetwork.ai/learn/nptel/111107098/558dacad646e) (YouTube) 44. [Convergence of Z- transform](https://invisiblenetwork.ai/learn/nptel/111107098/8de236ee9af6) (YouTube) 45. [Application of Z-transforms-I](https://invisiblenetwork.ai/learn/nptel/111107098/1a1c7b744e53) (YouTube) 46. [Applications of Z- transform- II](https://invisiblenetwork.ai/learn/nptel/111107098/44983619352f) (YouTube) 47. [Fourier Series and its Convergence-I](https://invisiblenetwork.ai/learn/nptel/111107098/85d450479010) (YouTube) 48. [Fourier Series and its Convergence-II](https://invisiblenetwork.ai/learn/nptel/111107098/42a7e5102d62) (YouTube) 49. [Fourier Series of Even and Odd functions](https://invisiblenetwork.ai/learn/nptel/111107098/bf7b83004018) (YouTube) 50. [Fourier half-range series](https://invisiblenetwork.ai/learn/nptel/111107098/ad4a0beb9248) (YouTube) 51. [Parseval’s Identity](https://invisiblenetwork.ai/learn/nptel/111107098/17c73229f624) (YouTube) 52. [Complex form of Fourier series](https://invisiblenetwork.ai/learn/nptel/111107098/641fa5b2d9ad) (YouTube) 53. [Fourier integrals](https://invisiblenetwork.ai/learn/nptel/111107098/ae8b8cd94993) (YouTube) 54. [Fourier sine and cosine integrals](https://invisiblenetwork.ai/learn/nptel/111107098/6e0ee9e9e416) (YouTube) 55. [Fourier transforms](https://invisiblenetwork.ai/learn/nptel/111107098/df49c105f7b9) (YouTube) 56. [Fourier sine and cosine transforms](https://invisiblenetwork.ai/learn/nptel/111107098/2656bdde9e0a) (YouTube) 57. [Convolution theorem for Fourier transforms](https://invisiblenetwork.ai/learn/nptel/111107098/0e7c9bb4beed) (YouTube) 58. [Applications of Fourier transforms to BVP–I](https://invisiblenetwork.ai/learn/nptel/111107098/575f2d2b4c51) (YouTube) 59. [Applications of Fourier transforms to BVP–II](https://invisiblenetwork.ai/learn/nptel/111107098/b2862bfad7a5) (YouTube) 60. [Applications of Fourier transforms to BVP–III](https://invisiblenetwork.ai/learn/nptel/111107098/35764f16df9f) (YouTube)